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Volumn 415, Issue 1, 2006, Pages 114-139

A geometric theory for preconditioned inverse iteration IV: On the fastest convergence cases

Author keywords

Elliptic partial differential operator; Inverse iteration; Multigrid; Preconditioner; Rayleigh quotient; Symmetric eigenvalue problem

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; LINEAR ALGEBRA; MATHEMATICAL PROGRAMMING; MATHEMATICAL TECHNIQUES; PARTIAL DIFFERENTIAL EQUATIONS;

EID: 33645140923     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2005.06.022     Document Type: Article
Times cited : (9)

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  • 2
    • 0035586115 scopus 로고    scopus 로고
    • A geometric theory for preconditioned inverse iteration. I: Extrema of the Rayleigh quotient
    • K. Neymeyr A geometric theory for preconditioned inverse iteration. I: Extrema of the Rayleigh quotient Linear Algebra Appl. 322 2001 61 85
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    • Neymeyr, K.1
  • 3
    • 0035585865 scopus 로고    scopus 로고
    • A geometric theory for preconditioned inverse iteration. II: Convergence estimates
    • K. Neymeyr A geometric theory for preconditioned inverse iteration. II: Convergence estimates Linear Algebra Appl. 322 2001 87 104
    • (2001) Linear Algebra Appl. , vol.322 , pp. 87-104
    • Neymeyr, K.1
  • 4
    • 32044463478 scopus 로고    scopus 로고
    • A geometric theory for preconditioned inverse iteration. III: A short and sharp convergence estimate for generalized eigenvalue problems
    • A. Knyazev, and K. Neymeyr A geometric theory for preconditioned inverse iteration. III: A short and sharp convergence estimate for generalized eigenvalue problems Linear Algebra Appl. 358 2003 95 114
    • (2003) Linear Algebra Appl. , vol.358 , pp. 95-114
    • Knyazev, A.1    Neymeyr, K.2
  • 5
    • 0000522446 scopus 로고    scopus 로고
    • Preconditioned eigensolvers-an oxymoron?
    • A. Knyazev Preconditioned eigensolvers-an oxymoron? Electron. Trans. Numer. Anal. 7 1998 104 123
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  • 6
    • 0344845742 scopus 로고    scopus 로고
    • A subspace preconditioning algorithm for eigenvector/eigenvalue computation
    • J. Bramble, J. Pasciak, and A. Knyazev A subspace preconditioning algorithm for eigenvector/eigenvalue computation Adv. Comput. Math. 6 1996 159 189
    • (1996) Adv. Comput. Math. , vol.6 , pp. 159-189
    • Bramble, J.1    Pasciak, J.2    Knyazev, A.3
  • 7
    • 0036003403 scopus 로고    scopus 로고
    • A geometric theory for preconditioned inverse iteration applied to a subspace
    • K. Neymeyr A geometric theory for preconditioned inverse iteration applied to a subspace Math. Comput. 71 2002 197 216
    • (2002) Math. Comput. , vol.71 , pp. 197-216
    • Neymeyr, K.1
  • 9
    • 0000057534 scopus 로고
    • The steepest descent method for an eigenvalue problem with semi-bounded operators
    • B. Samokish The steepest descent method for an eigenvalue problem with semi-bounded operators Izv. Vyssh. Uchebn. Zaved. Mat. 5 1958 105 114 (in Russian)
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  • 10
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  • 12
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    • Iteration methods in eigenvalue problems
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  • 13
    • 33845535476 scopus 로고
    • Minimization of the computational labor in determining the first eigenvalues of differential operators
    • E. D'yakonov, and M. Orekhov Minimization of the computational labor in determining the first eigenvalues of differential operators Math. Notes 27 1980 382 391
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    • Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method
    • A. Knyazev Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method SIAM J. Sci. Comput. 23 2001 517 541
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* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.